help-36

[digital crescent]

3

[warm ether]

if it has 1 it would just be 3

[digital crescent]

im pretty sure the 0's count as well

[warm ether]

3*10^-7

they do, yeah

[turbid sable]

So zeros after the decimal count as a sig fig but not 0s before the decimal point

[warm ether]

its a bit more complicated than that

0.0054 has 2 sf

but if i just wrote 0.00 then thats also 2

if theres no non-zero after the front zeros, then yes every zero after the point is a sf

[final saddle]

@turbid sable Has your question been resolved?

[turbid sable]

I see

Btw or the very last question what is the calculation to find this out

The distance is 4.068 * 10^13 btw

<@&286206848099549185>

[tranquil pine]

whats the unit

[turbid sable]

Km

[tranquil pine]

no specific formula, but find how many hours it would take and then divide by 8760 (number of hours in year)

[turbid sable]

Thanks Lyn

.cloe

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[next pagoda]

This isn't a vector right?

[neon fulcrum]

Why not?

[final saddle]

@next pagoda Has your question been resolved?

[next pagoda]

It doesnt have the typical notation that I've seen.

<>

[neon fulcrum]

Angle brackets isn't the only notation for vectors y'know

These are vectors

[next pagoda]

What other notation is there

That's what we use

How do you know

[neon fulcrum]

i j and k

3 basis vectors

And a x b

Cross product

It could be other things, but it being vectors makes most sense to me

[next pagoda]

I see

I gussed it might be a vector but there wasn't any notation telling me it was

but that was because this section is all about vectors

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[next pagoda]

Where did I make a mistake?

[distant ridge]

I've never seen that way to compute determinants

[distant ridge]

you're swapping the order you compute it

[next pagoda]

oh

I guess I should re read how to perform this

I wasn't aware that the order mattered but I can see that it does!

ty

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[rancid kayak]

hi

[rancid kayak]

i thought this was simple like find the sf then time the are but its not and im not sure

[lusty sapphire]

well, u gotta understand what similar means

[rancid kayak]

same shape but different size right?

[lusty sapphire]

yes but that should help u somehow

they are also giving u R surface

[rancid kayak]

yep

[lusty sapphire]

so figure out the relation

try with a simple shape, draw ur own rectangle

[rancid kayak]

ok

[lusty sapphire]

give it some lengths, calculate its surface

and then draw a similar one

and see how it goes

[molten remnant]

isnt it 2x= 14 then x = 7

or am I wrong

[rancid kayak]

lol idk

[lusty sapphire]

idk if u are wrong, but shut up. U dont help anyone spoonfeeding

[molten remnant]

Woah-

[rancid kayak]

ok i drawed the rectangle

<@&268886789983436800> not sure whats going on//

[molten remnant]

?

[rancid kayak]

can you help me/

[molten remnant]

did u find out the relation

b/w the two figures

[brisk charm]

Please don't tell people to shut up, you can tell people not to give away the answer in a more polite way

And yeah don't give away answers, try to lead them to the answer themselves

[molten remnant]

Aight mb

[rancid kayak]

so scale factor is7\

[molten remnant]

yeah right

[rancid kayak]

whats next how do i relate that to the area

[molten remnant]

they've given u the area of the smaller one

[rancid kayak]

yes

[molten remnant]

so try to find the bigger area using the smaller

and given tuff

like u found the relation b/w the sides

now turn the relation of sides into the area

and multiply em

to get the area of the bigger pentagon

[rancid kayak]

nvm

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[safe portal]

I need some help

[stone wagon]

hint: find the circumference of the wire drum

[safe portal]

9.424

[molten remnant]

yeah thats right

[safe portal]

What do I do from there?

[molten remnant]

procedure?

find out the number of rotations

[stone wagon]

it's better to express it with its precise value, but that works too
next, find how many times this circumference "fits" in the 150 feet

[molten remnant]

by the drum

[safe portal]

I see

I got it

Thanks

I just have one more problem to solve

[molten remnant]

oh

[molten remnant]

u should first try making a diagram

[final saddle]

@safe portal Has your question been resolved?

[final saddle]

@safe portal Has your question been resolved?

[turbid sable]

What is the question? @safe portal

[safe portal]

This

[safe portal]

This one

[safe portal]

I figured it out

I'm good

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[elfin bough]

How do i get measure of XV

[elfin bough]

I tried but

Idk what I did wrong , my answer didn’t match up with andwer

I separated triangles

[muted prairie]

Where is 14 coming from

[elfin bough]

10+4

[muted prairie]

XZ has a length of 10, not 14

[elfin bough]

Oh

Bruh

💀

I didn’t see that line smh

[muted prairie]

rip

[elfin bough]

I thoigjt ZY was 10

Whoopsies

Okay thank you

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[hidden kiln]

can someone help me with this question pls

[white depot]

Show that 3/4 + √7/4 i is a solution for the equation 2z^2 -3z +2 = 0

If someone could help I would appreciate

[fallen vigil]

go to another channel

I could maybe help you if I knew if whom was referring to men or women 😭

[hidden kiln]

i know that this question is a bit ambiguous

but i think its 40% of men

as 'men' was the last subject mentioned

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[tranquil pine]

why is this not true

[tranquil pine]

what im thinking is, cos(5\pi/6) = -1/2, so 2 + 2(-1/2) = 1 for numerator.

then for denominator, sin(5\pi / 6) is \sqrt(3)/2

how should this be written out?

[final tangle]

you've messed up your special ratios

your sin and cos of 5pi/6 are incorrect

[tranquil pine]

oh yeah, the cos should be -\sqrt(3)/2

sin should be 1/2

so...

4-2\sqrt(3) ?

YEAHH

@final tangle thanks

.solved

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[lyric nebula]

can anyone help with this, not sure how to solve for a? like im unsure how to approach this when the bases are 2x2 matrix instead of single column

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[foggy fable]

can someone help me with this

[foggy fable]

so what I was thinking is write is as a summation and try to find a genereal formula for u v and w

[vital surge]

are we allowed to use calculus here

if yes, i'd recommend..

[foggy fable]

uhh what u mean by calculus

isn't that the name of the book

[vital surge]

i have no idea what you refer to...

"book" ? this is your resource not mine i have no idea where this problem comes from

i suggested calculus since that is easiest way to do this i believe. but asked since sometimes teachers like to impose tool restrictions

[foggy fable]

oh calculus is a tool? I was refering to calculus as my book is called calculus so a bit confused

[vital surge]

uh

[foggy fable]

uhm I assume it's prob meant to do like by hand i think

[vital surge]

do you know what calculus is?

[foggy fable]

not realy

[vital surge]

but you have a calculus book

[foggy fable]

I thought it was just math

[vital surge]

did you skip to a random page

[foggy fable]

the book is called calculus

[foggy fable]

not realy it was just some homework

but it was at the problem plus page

so I assume it's harder then normal

[vital surge]

so is this problem part of your homework?

[foggy fable]

not realy but it was one excercise up so I thought I wanted to give it a try

[vital surge]

it would be fairly difficult to do this problem wihout using calculus...

[foggy fable]

this one needs tool to solve the problem?

[foggy fable]

I see if I do calculus how do I solve it

like I was thinking e^x = summation of x^n / n! right

[vital surge]

calculus is not a "tool" so to speak.. it is an entire branch of mathematics

[foggy fable]

oh

[foggy fable]

so like uhm how do I usei t

[vital surge]

well i can't teach you calculus in the span of 30 minutes

[foggy fable]

oh it's like that?

so same like algebra

there is calculus?

[vital surge]

uh

i'm confused on how you have a calculus book but don't know what calculus is

is this not explained in the book?

[foggy fable]

don't think so my teacher also never said smth about calculus

but the book is called calculus tho

it's the 9th edition

[foggy fable]

oh u mean taking dervatives?

I can do that

[vital surge]

do you know what implicit differentiation is?

[foggy fable]

yes

you basically take the derivative of left side and right side

[foggy fable]

I gotta do that ?

oohh I think I see what u mean

use implicit differentation to uget to u v w

and then just plug it in

[foggy fable]

wait how do I deriviate the u * v * w part it's like product rule with 3 elements

nvm I think I know it

u get 9 terms right

[vital surge]

yes you treat u, v, and w as functions

[vital surge]

i don't think so

[foggy fable]

uh

[foggy fable]

wait 3 terms right?

u take the partial derivative in each function

so u get 3 terms I think

[vital surge]

you would be better off just sending what you have

[foggy fable]

well I gotta differentaite 3 times right

I just did it once

[vital surge]

what is your reasoning for this?

[foggy fable]

uhm after doing it 1 time I still got 3 * u^2 * u' etc

so like to get u^2 to change to u

[foggy fable]

oh wait 2 times

right?

[vital surge]

no

if you differentiate more, you will only be adding more complicated derivatives of u, v, w to your expression

[vital surge]

now look back at what u, v, and w are...

[foggy fable]

but I still can't plug it in because of the square

[vital surge]

i did not say plug it in

now i ask how are u, v, and w related to each other

[foggy fable]

if u add them they become e^x I think

right?

[vital surge]

that is correct... and what else

[foggy fable]

u want the radius of convergence?

or what u mean

[vital surge]

no

i am asking how they are related to each other

[foggy fable]

uhm

they have similair pattern

[vital surge]

that is also right

[foggy fable]

it's just u = x^3n / 3n!

v =

[vital surge]

ok now hold on

[vital surge]

look back at what you got after applying implicit differentiation

[foggy fable]

it's a long expression btw

[vital surge]

why is that relevant?

[foggy fable]

uh I guess it's not

but when I look at it

idk what I am supposed to see

[vital surge]

so you have a bunch of squares like u^2 and differentiated terms like u'

[foggy fable]

yes

[vital surge]

is there anything at all you can do with either of these terms

[foggy fable]

so I guess it has to be to delete the u' someway

like when I do u'

oh wait

I see it

u' = w

right?

v' = u

and w' is v

[vital surge]

yes that is good

[foggy fable]

am I in right direction

[vital surge]

and the solution becomes fairly straightforward once you see this

[foggy fable]

wait

[vital surge]

so try complete problem

i stay here if needed

[foggy fable]

I still don't see it

wait I write it out first

maybe that helps

[vital surge]

you need to do that

i assumed you already wrote it out because you said it was "long"

[foggy fable]

I mean the derivative = part

[foggy fable]

oh I see it

they cancel eachother out

it becomes 0

[vital surge]

that is true

[foggy fable]

how did u knew it so well

did u made this excerrcise before?

and also did u wrote it out or did u do it in ur head everytihng

[vital surge]

the most important observation is the cyclic derivatives

[vital surge]

not mental...

never mental math for problem like this

always always write with pen/paper or with digital device

[foggy fable]

I haven't heard of cyclic derivatvies

[foggy fable]

u use pen/paper or digital device?

[vital surge]

wdym

it doesn't matter what is used

my point is when doing problems it always helps to write out your work

i would never attempt a problem like this mentally unless i was very confident in my method

[vital surge]

this is not a real topic btw... i just call it "cyclic derivative" because that is exactly what it is

the derivatives of u, v, w are "cyclic" with each other

[foggy fable]

I see but I feel like problem like these the hard part is to come up with doing the implicit differntation but I couldn't see that

[vital surge]

yes that is true

[foggy fable]

cyclic with eachother as in the derivative of one is the expression of another

[vital surge]

yes

[foggy fable]

I see

[vital surge]

"cyclic" in math is a word with a somewhat loose meaning

if things sort of go in a loop, you can refer to just about anything as "cyclic"

[vital surge]

although sometimes for harder problems there is not much better solution than "this sort of makes sense? but i don't know. so, i try it and see what happens"

[foggy fable]

ye I was also trtying but this chapter was about series and u v and w added to eachother is e^x so I thought

it had to do smth with e^x

[vital surge]

maybe there is a good way of doing this problem using a series interpretation

but that sounds hard / strenuous

if this problem is in chapter with series then maybe it is true

but it is also possible they just put this problem in a series chapter because the problem involves series

[foggy fable]

ye most of times there are multiple ways but ye I am just satisfied if I know 1

[foggy fable]

ye but it's also in the problem plus section

so most of times it's not just easily doing 1 step

[vital surge]

interesting

[foggy fable]

anyways I appreciated the help, saved alot of frustration lol

[vital surge]

welcome 🙂

sometimes nice to see people ask about "unusual" questions like these

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[final saddle]

Please don't occupy multiple help channels.

[tranquil pine]

the integration of x^3 is x^4/4
3^4 is 81
81/4 - 0
81/4 is multiplied by 1/3 (1/b-a) for MVT
But that gave me the wrong answer 🙁

[tranquil pine]

I deleted the other one

[lyric summit]

you have to find the value of c

[tranquil pine]

Yeah I got 81/4 after doing that

But it was wrong

These are the answers

[lyric summit]

that is the same as in your book

[tranquil pine]

I'm not sure what I did wrong

[lyric summit]

numerator and

denominator

were multiplied by cube root of 2

[tranquil pine]

I messed up in the numerator seems like

@lyric summit

[lyric summit]

still cant see it >

[tranquil pine]

What did I even do wrong

[lyric summit]

?

[tranquil pine]

No the answer makes sense now

But

Ok

[lyric summit]

your integral gave you 81/4 then you multiplied by 1/3

and you get

27/4

and then you have what i wrote for you

f( c ) = c^3

[tranquil pine]

Ohhh

That's what I forgot to do

Multiply by the 1/3

[lyric summit]

smiles

[tranquil pine]

Thank you so much!

[lyric summit]

yvw)

[tranquil pine]

.close

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[fallen comet]

i tried to do it but idk what to do

i got the force of the weight of the beam i think

or wait no

i got the torque of it

i think

idk

actually i think i got nothing

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@fallen comet Has your question been resolved?

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@fallen comet Has your question been resolved?

[fallen comet]

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[sacred egret]

How do I factor this

[tranquil pine]

Do you know the quadratic equation?

[sacred egret]

Yeah but it don’t help

[pliant shore]

Have you been taught the AC method?

It's basically multiply by 3 here

[sacred egret]

No clue what that is

[pliant shore]

You get (3x)^2 - 2(3x) - 15 = 0

[sacred egret]

I only know the box method

[pliant shore]

And if you sub u = 3x

You get u^2 - 2u - 15 = 0

Which is much easier to factor

[sacred egret]

I’m lost in the sauce rn

[pliant shore]

I skipped a few steps

Okay so if you multiply everything by 3 what do you get?

[sacred egret]

3x^2-6x-15=0?

[pliant shore]

You need to multiply 3x^2 by 3 too

So 9x^2

Now notice 9 is a perfect square

So 3x × 3x = 9x^2

(3x)^2 = 9x^2

[sacred egret]

Okay

Got it now

[pliant shore]

Npnp

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[final venture]

where did (-4) * 3^n come from?

[pliant shore]

The particular solution

It has to be in the form constant * 3^n

Cause when you sub n + 1 and n + 2 you also get multiples of 3^n

[final venture]

so we have xn^p= an^3?

[pliant shore]

Yeah the particular solution is A 3^n

Not n^3

[final venture]

yeah sry

oaky thanks i forgot about that

[pliant shore]

Npnp

[final venture]

.close

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[long ether]

Not sure what the easiest way to go about this is

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@long ether Has your question been resolved?

[long ether]

.close

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[final saddle]

Please don't occupy multiple help channels.

[waxen thistle]

can someone help me proove this

i asked in the other channel ive been waiting 40 mins no one

[alpine burrow]

Because Angle 1 is congruent to angle 3
So Angle 1+2=Angle 3+2
So angle AED must be congruent to angle BEC. (it's just like adding numbers together, for example, if a=b then a+c=b+c)

[alpine burrow]

Set the price of that item before discount is x. We have the following equation:
x-20%*x=60
=> x-0.2x=60
=>0.8x=60
=>x=60/0.8=75
So the price of the item before discount must be $75.00.

[final saddle]

@waxen thistle Has your question been resolved?

[long ether]

Thank you!!

[alpine burrow]

you're welcome, close this channel

[long ether]

It's not my channel anymore. It's @waxen thistle s channel

[alpine burrow]

oh yea

[final saddle]

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[hidden kiln]

Can someone help me with this question pls

[vestal sentinel]

!status

[final saddle]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

@hidden kiln Has your question been resolved?

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[vocal coyote]

yo can someone tell what the pattern is when u keep multiplying multiples of 2 by 2 i know the last digit will always be 2,4,8 or 6 but theres more to it no?
like whats the rule

[cloud blade]

Let's say we have 2^x
If you divide x by 4 and get a remainder of 1, the ending digit is 2
If you divide x by 4 and get a reminder of 2, the ending digit is 4
If you divide x by 4 and get a remainder of 3, the ending digit is an 8
If you divide x by 4 and get no remainder, the ending digit is a 6

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[vocal coyote]

then what would the rule be?

[final saddle]

@vocal coyote Has your question been resolved?

[vocal coyote]

<@&286206848099549185>

[final tangle]

they said the rule,

not sure what else you're expecting

[final saddle]

@vocal coyote Has your question been resolved?

[vocal coyote]

oh sorry i miss understood it

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[tired knot]

Im back,
Sorry,
I dont understand how the red works

How they got -2 to become a positive

[gentle aspen]

Rhs you have 1024 which is positive

So lhs must be positive

[tired knot]

But how can you do that

Isnt that like illegal

Like it isnt math

[ocean mortar]

It's still logic

For that to be true, it has to be positive

[gentle aspen]

Why it is not math

?

You made an observation

[inland kettle]

logic is a crucial part of maths

[tired knot]

Wont they have to state x>0

something like that

[inland kettle]

its literally what all of it is based on

that's just a formality

[gentle aspen]

X??

[tired knot]

n*

well acc no

[ocean mortar]

If the question requires it, sure. But n is always positive since it's just the number of terms

[tired knot]

n is a seires and its always +tive

[gentle aspen]

n is obviously greater than 0

[ocean mortar]

Point is if (n-1) is even or odd

Here, (n-1) has to be even

[gentle aspen]

You wanted to say n is odd ig

[ocean mortar]

It would have been a contradiction if (n-1) were odd

But you can't reach that without making the right assumptions

[gentle aspen]

Right

They wanted you to make that observation

[ocean mortar]

Your right side is positive, you have to assume left side is positive to move forward

^^yep

[tired knot]

Ok, just because im a bit new to 'making observations' as I never rlly had to do that

How would the question be formated

To make +2 into a -2

[gentle aspen]

Nvm now youll be able to do that

[tired knot]

is it just if its -1024?

[ocean mortar]

Split the (-1)^(n-1) from the term and use words like they did in the comment

[gentle aspen]

Ya

[ocean mortar]

Had it been -512 instead

Then you would have -2^(n-1)

And that would have checked out

There, n-1 would be 9, n would be 10

[tired knot]

ok this is very interesting to me

Ill have to do a few more questions on this

to understand properly

[ocean mortar]

It's still correct what you did, but in the end you have to be careful about it, if it magically ended were n-1 = 11, then that's broken

Obviously it won't happen in this case

[ocean mortar]

Yeah, you'll pick it up, it's not too tough

[tired knot]

Alright

Thank you once again

[ocean mortar]

No problem

[tired knot]

.close

[final saddle]

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[fossil bronze]

what am i doing wrong?

[inland kettle]

it clearly states

if you want to write abs x use "abs (x)"

[unreal anvil]

missing an x?

[final tangle]

show work

[fossil bronze]

i tried it that way and it didn't work

1 sec

[final tangle]

your approach to pfd is incorrect

A(x-1) + B(x+1)
won't result in a quadratic with constants A,B

also doesn't show how you ended up getting the value of 1/2 and -5/2

[fossil bronze]

i subbed in 1 and -1

what approach could i take?

[final tangle]

first recognise that the degrees of the numerator and denominator are the same,
so you should first start with long division

[fossil bronze]

ohh

there will be a remainder right?

[final tangle]

yes. and then you do pfd on remainder/divisor

[final saddle]

@fossil bronze Has your question been resolved?

[fossil bronze]

Is it 1 and -2x+3 as the remainder?

[final tangle]

yes

[fossil bronze]

now i can intergrate i see using partial?

[final saddle]

@fossil bronze Has your question been resolved?

[fossil bronze]

I got an answer but I am unsure whether it is right or wrong?

[worthy thorn]

Mention helpers

@( )helper
But without the space

[fossil bronze]

<@&286206848099549185>

[final saddle]

@fossil bronze Has your question been resolved?

[final tangle]

if you have work show it

none of us will know either
and will be unable to advise you on what to do next

[final saddle]

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[fleet maple]

what would be the double integral to evaluate the volume inside all the functions?

[fallow wren]

it is a supermario kar road ?

[fleet maple]

no tf

[final saddle]

@fleet maple Has your question been resolved?

[final saddle]

@fleet maple Has your question been resolved?

[final saddle]

@fleet maple Has your question been resolved?

[final saddle]

@fleet maple Has your question been resolved?

[final saddle]

@fleet maple Has your question been resolved?

[hazy veldt]

Why is your z coordinate parameterized in 2 different ways?

[final saddle]

@fleet maple Has your question been resolved?

[fierce orchid]

What is this program?

[fleet maple]

Its a website

3d plotter

[final saddle]

@fleet maple Has your question been resolved?

[steel cosmos]

.

[final saddle]

@fleet maple Has your question been resolved?

[whole halo]

you can also use https://desmos.com/3d to graph the functions

first, the x bounds
the lower x-bound and the upper x-bound are at the corners where all three graphs meet
so z = 1 - x^2, z = y, and y = x^2 - 3
1 - x^2 = z = y = x^2 - 3
1 - x^2 = x^2 - 3
4 = 2x^2
2 = x^2
x = ±√2
so the x bounds are -√2 ≤ x ≤ √2

then, the y bounds
the lower y-bound is y = x^2 - 3
the upper y-bound is the edge of where z = 1 - x^2 and z = y meet
z = y = 1 - x^2
so y = 1 - x^2 is the upper y-bound
so the y-bounds are x^2 - 3 ≤ y ≤ 1 - x^2

then, the z bounds
the lower z-bound is z = y
the upper z-bound is z = 1 - x^2
so the z-bounds are y ≤ z ≤ 1 - x^2

from this, the integral is $\int_{-\sqrt2}^{\sqrt2}\int_{x^2-3}^{1-x^2}\int_{y}^{1-x^2}\dd{z}\dd{y}\dd{x}$\
or $\int_{-\sqrt2}^{\sqrt2}\int_{x^2-3}^{1-x^2}((1-x^2)-(y))\dd{y}\dd{x}$

[soft zealot]

mtt07734

[final saddle]

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Channel closed

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[young coral]

I have a quick integral question

I just did it by hand then inputted it into Mathway and got the same answer but web assign says it’s wrong

Is there something I’m doing wrong or is there another way to write this answer

Nvm lmao I typed 366 instead of 336

.close

[silver roost]

Not sure about this, but maybe 6 is a cause you’re going up the same amount as the others but you’re also moving in x more

[buoyant kayak]

Hello, how are you? Excuse me if my English is not so good. Can someone explain to me the properties of logarithms, exponential functions, logarithmic functions and radical functions?

plis

[soft kindle]

is cos(-x) just going to be -cos(x)

[lapis wedge]

ye

[soft kindle]

so its considered an even function rite

wb sin(-x), is that also equal to -sin(x)?

[lapis wedge]

uh i’m not sure I just know -cos(x) = cos(-x)

[tranquil pine]

put it in #1021175428326633542

[lapis wedge]

I beilieve it is even tho

since the graph is symmetrical across the y axis I believe

sin would also be an even function I believe

[tranquil pine]

even more broken bot 😦

[lapis wedge]

uh oh

[tranquil pine]

much nicer when it was just not adding new channels lol

wait a second it might be fixed actually

[spring haven]

No

cosx is an even function

Meaning cos(-x)=cos(x)

sinx is an odd function, so sin(-x)=-sin(x)

[soft kindle]

does anyone know how to solve this

[cerulean radish]

,rotate

[cerulean radish]

what the fuck

[soft kindle]

samething i said and its on my alg 2 exam 😭

[cerulean radish]

what are b and c?

[soft kindle]

the two exponents

its x raised to the "b" and y raised to the "c"

[cerulean radish]

well what i can do is

help simplify your equation

if that helps then sure

[soft kindle]

sure

thats lowkey the point of the question anyways

[cerulean radish]

alright

so

lets look at the numerator first

its cube root

if you express that as an exponent

what would that become?

[soft kindle]

3y^3 cube root(y^2 x^2 sqrt(x))

[cerulean radish]

huh

ooh

okay

i was thinking you could express it as

$(27x^5/2 y^5)^(1/3)$

ugh weird ass bot

but u get what i mean

[soft kindle]

ye

[cerulean radish]

now u can write that as pretty much

(27x^5)^1/3 times (y^5)^1/3

correct?

thats that for now

[soft kindle]

mk

[cerulean radish]

now look at the denominator

if a power comes from denominator to numerator

what happens

<@&286206848099549185> need an individual to help the lad i gotta dip

[cyan apex]

Sorry to bother you but do you know why there's hardly any available math help? There's 1 vacant but it says owner is missing

[cerulean radish]

Not quite sure as such

[thorny coral]

can you help

[cerulean radish]

With what

[thorny coral]

algebra 2

[soft kindle]

how do you make this -r(x)

[final saddle]

@young coral Has your question been resolved?

[young coral]

[final saddle]

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[grave oyster]

Need help

[grave oyster]

idk where to start

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[pseudo nymph]

what would answer be

[pseudo nymph]

im confiused what our cases can be

i just guessed a

[final saddle]

@pseudo nymph Has your question been resolved?

[viscid stirrup]

Consider n=3, we have 1 way

n=4 we have 3 ways

n=5 we have 7 ways

For each n, we can build into subcases

For n=4, we have the sub case that 111 is at the end or beginning or at the end

Consider it at the beginning first

Then the last value has 2 choices (either 1 or 0)

Now considering what I said before, if 111 is at the end, remember it cannot start with a 1 otherwise we double count so there is 1 way

So for n=4, there are 2+1= 3 ways

Now for n=5, consider 111 at the very beginning, we get 2^2 ways to choose the end

If 111 was in the middle, considering the previous sub case we have to exclude the cases that have 1 at the beginning (since we already counted them), so 0 must be at the beginning and the end must have 2 ways

[pseudo nymph]

how is there 3?

[viscid stirrup]

1110, 1111 and 0111

[pseudo nymph]

ohh

11111, 11100, 00111, 01110, 011111, 11110, 01110, this is for 5?

[viscid stirrup]

Continuing from here, with in mind of the previous sub cases, if it ends in 111, remember it cannot have 1 and 1 at the beginning since we already counted that, so both beginning digits are 0 and 0 so we count this as 1 way

[viscid stirrup]

Yes

[viscid stirrup]

From there, the total number of ways for n=5 would be 4+2+1=7

So we previously saw that for n=4, it would be 2+1 and for n=5 it would be 4+2+1

The intuition here is that you keep on adding a power of 2 to the previous number, (particularly 2^(n-3)

So for n=6, it would essentially be the n=5 case and then plus 2^3=8

So 7+8=15

Notice that this is 2^(n-2)-1 for any n if you use the geometric series formula

So basically tn = 2^(n-2)-1

Here for t=5, we get 7, and t=6, we get 15

So this formula is correct

Now we can substitute this formula into each of the options and find which one is mathematically correct

Sorry, for my longwinded explanation, I am sure that there is a very simple way

I just wanted to derive a formula for Sn in your question

If you need any clarification, personally dm me because I gtg now, but I hope u find this somewhat helpful

And I hope someone else can give a simpler way as to how the recursion works for this problem!

cyaaa

[pseudo nymph]

ok thanks

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[thorny coral]

confused on what i did wrong

[tiny gorge]

your inverse function doesn't look right

if you plug in an x greater than 5 then you're taking the log of a negative number

[final saddle]

@thorny coral Has your question been resolved?

[thorny coral]

this look better?

[tiny gorge]

looks ok now

[thorny coral]

thanks for the help man it was correct

[tiny gorge]

nice

[thorny coral]

.close

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[dusky marten]

lol

[dusky marten]

.close

[final saddle]

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[dusky marten]

.reopen

[final saddle]

✅

[dusky marten]

.close

[final saddle]

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[dusky marten]

.reopen

[final saddle]

✅

[dusky marten]

.close

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[dusky marten]

.reopen

[final saddle]

✅

[dusky marten]

.close

[final saddle]

Channel closed

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Use .reopen if this was a mistake.

[dusky marten]

.reopen

[final saddle]

✅

[dusky marten]

.reopen

.close

[final saddle]

Channel closed

Closed by @dusky marten

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[pseudo knot]

<@&268886789983436800>

[sturdy ocean]

@dusky marten dont abuse help channels

[dusky marten]

ok

srry

[final saddle]

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[hoary oxide]

I got stuck on this question:

[hoary oxide]

This is what I did:

$$y=e^{2t}v$$
$$y'=e^{2t}v'+2e^{2t}v$$
$$y''=e^{2t}v''+4e^{2t}v'+4e^{2t}v$$

[soft zealot]

BigPenguin

[hoary oxide]

After that, I plugged in the corresponding y, y', and y'' to get:

$$e^{2t}(tv''+4v'+8v)$$

[soft zealot]

BigPenguin

[hoary oxide]

After that, I have no idea how to proceed.. apparently they say that the v' term is supposed to disappear if you do it correctly, but I triple checked my work and it always appears in the end? WHAT DID I DO WRONG!!!

[hoary oxide]

THIS IS DA QUESTION

[scarlet drift]

is this xyz?

[hoary oxide]

what?

what is xyz mean

[scarlet drift]

what program is this?

[hoary oxide]

this is LWTech HW

community college HW

dw I get 99 tries

I can show snip

[scarlet drift]

no i mean what program are yall using?

is this myopenmath?

[hoary oxide]

Canvas!

[scarlet drift]

canvas is the

nvm

lol

[hoary oxide]

can you please help me 🥺

I showed my work!!!!

WITH LATEX

[hoary oxide]

😭

[scarlet drift]

relax i'm reading rn

[hoary oxide]

omg yayyy

I am going to redo this problem from scratch!

[tiny gorge]

i just tried it and the v term cancels for me, your 8v is wrong

[hoary oxide]

in the meantime

[scarlet drift]

i was thinking

[hoary oxide]

wait what

[scarlet drift]

something was wrong with his eqn

[hoary oxide]

lemme reread

[hoary oxide]

wait is the first latex thingy I wrote correct tho?

[tiny gorge]

when you plug in all your crap, the terms involving v have this coefficient:
4t e^(2t) - (4t + 4) 2e^(2t) + (4t + 8) e^(2t)

and that equals zero

[hoary oxide]

shouldn't the v' cancel out, or just the v?

lemme get my paper

[tiny gorge]

my recollection of ode's is very slight, i had to look up the method
but according to paul's online notes:

first example here: https://tutorial.math.lamar.edu/classes/de/ReductionofOrder.aspx

[hoary oxide]

WAIT

WAHOO

[hoary oxide]

YOU ARE RIGHT

[tiny gorge]

nice

[hoary oxide]

$$te^{2t}v''-4e^{2t}v'$$

[soft zealot]

BigPenguin

[hoary oxide]

that is da final thingy I got

[hoary oxide]

ohhh so v drops out, not da v'

[tiny gorge]

and then i guess you do something like let u = v'?

[tiny gorge]

right

[hoary oxide]

wait why

OHHHH

[scarlet drift]

yeh

you're reducing the order

[tiny gorge]

to turn it into a afirst order equation

[hoary oxide]

I GET IT

[scarlet drift]

that way

[tiny gorge]

in u

[hoary oxide]

oh my god how are you so smart yall

I'm so jealous

I wish I could steal your brain

[tiny gorge]

nooo i need my remaining brain cells

[scarlet drift]

i mean i'm lookin at a book rn

[hoary oxide]

aight lemme do dis rn

wait is it better to do my work on paper

or latex

[tiny gorge]

i just googled reduction of order ode and it took me to paulie's

sometimes google is the brain you need

[hoary oxide]

🫡

[tiny gorge]

personal preference of course
i like to do latex unless there's much drawing/sketching/plotting involved

[hoary oxide]

u=t^4

[hoary oxide]

gotchya

[scarlet drift]

we usually skip reduction of order. that being said, you may find this useful in other problems. this is a general formula for finding the 2nd solution when you have the first one:

[hoary oxide]

what do you use?

like is there a fancy pancy latex website to notes thingy

[hoary oxide]

this seems so complicated

I think i'm just gonna forget it after a week haha

I'm gonna use the Bungo strat

[tiny gorge]

well i'm sure there are such things (like overleaf?) but i'm old school, i just have a local installation of texworks/miktex

[hoary oxide]

and not memrozie da formulas

[scarlet drift]

yeh that's fine. it comes from the base equation:

[tiny gorge]

that's not necessarily the optimal strategy, it's just my workaround for being very bad at memorizing things haha

[scarlet drift]

so it won't always work

[hoary oxide]

gotchya

I love you both very very much

< 3

[tiny gorge]

big penguin big heart haha

[scarlet drift]

so true lol

[hoary oxide]

wait guys

tragic news

it said I got the problem wrong

😭

wait lemme show you my work

WITH THE MAGIC OF

latex

[tiny gorge]

uh oh, the pressure is on

[hoary oxide]

$$te^{2t}u'-4e^{2t}u=0$$

[soft zealot]

BigPenguin

[hoary oxide]

(we turned it into a first order equation)

[tiny gorge]

i suppose you can cancel out those e^2t's

[hoary oxide]

$$\frac{u'}{u}=\frac{4}{t}$$

[soft zealot]

BigPenguin

[tiny gorge]

and then you have to stop procrastinating and actually solve a differential equation 😭

[hoary oxide]

shush you are stealing my thunder

[tiny gorge]

hahah

sorry sorry

[hoary oxide]

$$u=t^4$$

[soft zealot]

BigPenguin

[tiny gorge]

oh good old separation of variables

more or less the only technique i recall

[hoary oxide]

$$v=\frac{t^5}{5}$$

[soft zealot]

BigPenguin

[hoary oxide]

and since we know that

$$y(t)=v*y_1(t)$$

[soft zealot]

BigPenguin

[scarlet drift]

hold up

[hoary oxide]

WE GET

[scarlet drift]

u'/u = 4/t

what exactly did you do there?

[hoary oxide]

mhm

[hoary oxide]

so once we get this

we integrate both sides

ln(u)=4*ln(t)

u=t^4

[scarlet drift]

ok i'm tracking

keep goin

(still playing video games at the same time)

[hoary oxide]

SO ATFER THIS

we remember that y_1(t)=e^2t

[tiny gorge]

i fast forwarded past the boring parts and plugged in your t^4 and saw that it worked and happiness ensued

[scarlet drift]

LOL

[hoary oxide]

from all of the way up here!!!

so that means that the FINAL ANSWER

dun dun dun

should be t^5/5*e^(2t)

[tiny gorge]

oh yea you had to multiply that y1(t) back in

good recall

[hoary oxide]

$$\frac{t^5}{5}*e^{2t}$$

what da fuck

OHHH

[soft zealot]

BigPenguin

[hoary oxide]

YAY

[tiny gorge]

what's this * nonsense, you are not convolving

(or programming)

[hoary oxide]

but it said that I got the problem wrong when I plugged this in : (

[hoary oxide]

I love programming very much thank you

• is my bestie

[hoary oxide]

see I remember from trauma cause' a couple problems back I forgot to plug it in and then spent 30 minutes crying trying to figure out what i did wrong

[tiny gorge]

"give your answer in simplest form (ie no coefficients)" - might this be a clue?

[hoary oxide]

oh pls

wait lemme try

OH MY GOD

THIS IS THE STUPIDEST FCKING PROBLEM

[tiny gorge]

haha

[hoary oxide]

thank uuuuu

[tiny gorge]

the perils of software-graded assignments

[hoary oxide]

I hope you win your game 😎

[hoary oxide]

I miss linear algebra

so much cleaner

AND BEAUTIFUL

than diff eq

well except manually doing row reduced echelon form

[tiny gorge]

linear algebra is so nice and tidy compared with horrid differential equations

[scarlet drift]

XD

[lyric summit]

congrats 🙂 there is also generalisaiton:

[hoary oxide]

wait, the third part automatically follows the second part right?

[scarlet drift]

yeh showed em that earlier XD

[hoary oxide]

wait would I not have to memorize the third part of this thingy?

[tiny gorge]

all right, this has been a joy, but i'm overdue for hitting the hay

enjoy the rest of your ode assignment haha

[scarlet drift]

same. toodles

https://tenor.com/view/ドロン-忍法-パッと消える-poof-disappear-gif-15682669

[hoary oxide]

that is like saying "enjoy the rest of your torture"

smh

[tiny gorge]

very much like that

cheers

[hoary oxide]

I don't understand what the triple equal sign with the slash through it means

[lyric summit]

i jsut wrote a formula for the general solution of any such equations like yours, when you have known one of its solutions

y_1 is yours

and y_2 is seen in general form

since he general solution ius a lineaer combination

it is based on wronskian

so y_2 is everything

behind C_2

[hoary oxide]

uh

wait let me process this

[lyric summit]

this triple sign fo equality means = identity

[hoary oxide]

👀

[lyric summit]

sure

you can multiply it to reach the form you will like

[hoary oxide]

okay I got this

[hoary oxide]

so y_1 (the initial solution that we are given) can be derived by the second equation in your three-equation thing, correct?

[lyric summit]

you did very well with yoru way too, this what iw rote you can use everytyime if you need some very fast thing

[hoary oxide]

like we get y(t)=y_1(t)*integral stuff
where does the y(t) go exactly?

[lyric summit]

direclty to the initial equation of yours

[hoary oxide]

ohhhh got it

[lyric summit]

i omitted al details here just gave you final thing

[hoary oxide]

yah makes sense

[lyric summit]

but it works great if you make such quick tests

[hoary oxide]

the only confusion remaining is where did z(t) come from?

[lyric summit]

that is new vairable , i wud cal it as helpful one, or auxialiry one

you can usse other letter

look:

such 2 order eqautins

[hoary oxide]

ohhh I think I did v(t)

[lyric summit]

comes to 1 order euqstions

[hoary oxide]

but for you, z(t)

[lyric summit]

yes

[hoary oxide]

coem sto 😭

[hoary oxide]

wait I am going to copy paste this into my notes

Thank you so much Joanna!!!

< 3

[lyric summit]

yvw)

[final saddle]

@hoary oxide Has your question been resolved?

[final saddle]

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[gray acorn]

for the at what time does the rock hit the ground

Idk what to do after this

Because I used quadratic function which gives 0 = -16t^2 + 20t -875

And there’s no solution

[formal trail]

not sure why you designated the starting height as 875 feet below the ground but it certainly couldn't hit the ground from below like that

[gray acorn]

?

[formal trail]

plugging in t = 0 gives a starting position of -875 feet, i.e. 875 feet below ground

[gray acorn]

ahhhhh

right tyty